Comments on: Parallel speculative addition via memoization

By: conal

conal — Thu, 29 Nov 2012 03:46:32 +0000

Graham: thanks for the pointer to your paper and to carry save addition.

By: conal

conal — Thu, 29 Nov 2012 03:45:26 +0000

Geoffrey & Lennart: Thanks! I'll dig into these parallel prefix approaches.

By: augustss

augustss — Wed, 28 Nov 2012 22:25:39 +0000

Conal, I think Geoffrey is referring to one of the standard multibit adders which works by parallel prefix, but replacing the full adder by an associative operator.

By: GrahamHutton

GrahamHutton — Wed, 28 Nov 2012 22:17:15 +0000

Hi Conal – have you looked at ‘carry save addition’, which uses an alternative representation of binary numbers to avoid the rippling carry in addition? Many moons ago myself and Erik Meijer wrote a paper about this: http://www.cs.nott.ac.uk/~gmh/basics.pdf. It would be nice to see how this could be expressed using more modern FP ideas.

By: conal

conal — Wed, 28 Nov 2012 19:02:31 +0000

Hi Geoffrey. I'm glad you brought up parallel prefix sum, and more generally scans, which I wrote about here recently. As I understand them, parallel prefix (aka "prefix scan") circuits add many numbers and produce sums of all prefixes (and more generally, associative operations, as you mentioned). The tricky bit is efficiently calculating all of the prefix sums, maximizing parallelism (to reduce time) and minimizing redundant computation (to reduce work). If one wants just a single result, then a balanced tree fold is much simpler and faster.

In contrast, the problem I'm considering here is to add just a pair of numbers operating on the multiple bits in parallel, producing a single, multi-bit sum. I don't know whether there are any interesting connections between pair addition and either scan or fold.

By: Geoffrey Irving

Geoffrey Irving — Wed, 28 Nov 2012 05:25:58 +0000

It's probably worth mentioning the way addition (and similar associative operations) are normally parallelized, namely parallel prefix circuits.